Integers Word Problems worksheet with three questions involving real-life scenarios and a website link for more resources.

Let's solve each question step by step.

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Question 1:

In a school exam, Rohan’s score was up to 500 points. Then he scored -100 points in the words category. What was his score then?

#### Solution:
Rohan's initial score is 500 points. He then scores -100 points, which means he loses 100 points from his current score. To find his final score, we subtract 100 from 500:

\[
500 + (-100) = 500 - 100 = 400
\]

So, Rohan's final score is:

\[
\boxed{400}
\]

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Question 2:

Kamla has gone for a hiking trip. She ended a hike at an elevation of 5,000 feet above sea level. She had started at an elevation of 5,000 feet above sea level. Which integer represents Kamla's change in elevation?

#### Solution:
Kamla started her hike at an elevation of 5,000 feet and ended her hike at the same elevation of 5,000 feet. Since her starting and ending elevations are the same, there is no change in elevation. The change in elevation is:

\[
5,000 - 5,000 = 0
\]

So, the integer that represents Kamla's change in elevation is:

\[
\boxed{0}
\]

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Question 3:

Tell whether the following statements are always true, sometimes true, or always false.

#### Part (a):
If a positive is subtracted from a negative integer, the difference is a negative integer.

#### Solution:
Let's consider a general case where we subtract a positive integer \( p \) from a negative integer \( -n \):

\[
-n - p = -n + (-p) = -(n + p)
\]

Since \( n \) and \( p \) are both positive integers, \( n + p \) is also a positive integer. Therefore, \( -(n + p) \) is a negative integer. This means the difference is always negative.

So, the statement is:

\[
\text{Always true}
\]

#### Part (b):
If a positive integer is subtracted from a positive integer, the difference is a positive integer.

#### Solution:
Let's consider a general case where we subtract a positive integer \( p_2 \) from another positive integer \( p_1 \):

\[
p_1 - p_2
\]

The result depends on the values of \( p_1 \) and \( p_2 \):
- If \( p_1 > p_2 \), then \( p_1 - p_2 \) is positive.
- If \( p_1 = p_2 \), then \( p_1 - p_2 = 0 \).
- If \( p_1 < p_2 \), then \( p_1 - p_2 \) is negative.

Since the result can be positive, zero, or negative depending on the values of \( p_1 \) and \( p_2 \), the statement is not always true.

So, the statement is:

\[
\text{Sometimes true}
\]

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Final Answers:

1. \(\boxed{400}\)
2. \(\boxed{0}\)
3. (a) Always true, (b) Sometimes true

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Thus, the final boxed answers are:
\[
\boxed{400, 0, \text{Always true, Sometimes true}}
\]